Thermal, Emi and Modern Physics Revision 1

8/6/2019 Thermal, Emi and Modern Physics Revision 1

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HCI P26 (a) The tip of a Scanning Tunnelling Microscope (STM) probe is positioned at a

distance d above a sample surface which has an energy difference, U - Eof6.0 eV between the potential barriers height and the most energetic electrons atits surface.

(i) Calculate the value of dat which the tip-surface transmission coefficient Tis 0.0001.0.368

[2]

(ii) Suppose d decreases by 1 %, calculate the percentage change intransmission coefficient, T.9.66 or 9.73 % [2]

(b) Explain how the STM maintained at a fixed vertical position is used to obtainatomic scale images. [2]

7 This question is about the homopolar generator.

In principle, a homopolar generator consists of a conducting disc spinning about anaxis in a magnetic field parallel to this axis. When the spinning disc is stoppedsuddenly, all its kinetic energy can be used to generate a large current surge.

In order to spin the disc, a d.c. power supply is connected as shown in Figure 7.1. Themagnetic force on the disc due to the current passing from the axle to the rim of theconducting disc provides the necessary accelerating force. As the conducting discspeeds up, however, there is an increasing voltage generated across the terminals T 1

and T2. When the power supply is disconnected, this voltage can be used to drive acurrent through a resistor connected between them as shown in Figure 7.2.

Figure 7.1 Figure 7.2


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The magnitude of the voltage Vcan be calculated from the relationship

kBrrV ad )(22 =

where rdand raare the radii of the disc and axle respectively, and Bis the magnetic fluxdensity, assumed to be uniform over the surface of the disc.

The homopolar generator is used as a research tool to produce a huge surge of currentwhen their terminals are suddenly short-circuited. One large homopolar generator inAustralia, which is designed to produce a large current surge, measures 3.6 m indiameter, rotates at 15 Hz and is so massive that the kinetic energy it stores at thisspeed is 580 MJ. When it is short-circuited, the current surge is used to produce short-lived but extremely high magnetic fields in order to study the properties of matter underextreme conditions. It is proposed that such fields could be used in an electromagneticgun to project a small mass to speeds of over 7 km s-1. This speed is of the order of thespeed of satellites in low orbits and hence the projected masses could be used to studythe problems encountered by missiles re-entering the atmosphere.

(a) What is meant by the term short-circuited as used in the passage? [1]

(b) (i) Explain why there is an increasing voltage generated between terminals T1and T2 when the conducting disc speeds up. (Paragraph 3) [2]

(ii) Is the output of a homopolar generator a.c. or d.c.? [1]

(iii) Give two applications which are suggested in the passage for the hugesurges of current produced by a homopolar generator. [2]

(c) Figure 7.3 shows a current surge from a short-circuited homopolar generator.

Figure 7.3

(i) Estimate the charge that flows during this surge.2.4 3.1 MC [3]

(ii) Calculate the maximum power dissipated when the terminals T1 and T2 of

the generator, which has an internal resistance of 0.12 m, are connectedtogether through a negligible external resistance.3.3 x 108 W

[1]


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(d) Using kBrrV ad )(22 = , determine the units for k. Hence, suggest what physical

quantity may be represented by the symbol k.s-1

[3]

(e) Describe the energy transformations that take place in the process shown in

(i) Figure 7.1 [1]

(ii) Figure 7.2 [1]

HCI P3

2 (a) Define the tesla. [1]1 Tesla is a unit of the magnetic flux density of a magnetic field if the force acting perunit length on an infinitely long conductor carrying a current of 1 A and placedperpendicular to the magnetic field is 1 N m-1.

(b) At the equator, a thin coil of 50 turns and of diameter 10.0 cm is in a vertical plane(with axis in the East-West direction) as shown in Figure 2.1. A compass, which is ina horizontal plane, has its pivot coinciding with the centre of the coil. Initially, nocurrent flows through the coil and the compass is pointing North as shown.

The magnetic flux density at the centre of a thin coil follows the formula2R

NB 0

I= ,

where Irepresents the current, Nthe number of turns of coil and Rthe radius of thecoil. The Earths magnetic field is 50.0 T.

Figure 2.1

When a current of 100 mA flows in a clockwise direction as viewed from the West,determine(i) the magnetic flux density, Bc, and its direction at the centre of the coil, due only

to the current flowing in the coil.6.3 x 10-5 T East [2]

N

S

EW


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(ii) the resultant magnetic flux density at the centre of the coil, BR, and the new

direction (angle from the North) which the compass will be pointing.8.0 x 10-5 T 51.6

[2

(c) A powerful electromagnet produces a uniform field in the gap between its poles, eachof which measures 4.00 cm 4.00 cm and are facing each other. There is no field due

to the electromagnet outside the gap. The circular coil in (b) is placed between thepoles such that its plane is perpendicular to the field lines and encloses all the fieldlines, as shown in Figure 2.2.

Figure 2.2

The magnetic field produced by the electromagnet is adjusted so that the field strengthsteadily decreases from 0.40 T to zero in 0.50 s. Calculate the e.m.f. generated in thecoil.0.064 V

[2

4 Diodes used in rectifying alternating current to direct current are p-n junctions made ofsemiconductors. A p-n junction is formed when p-type and n-type extrinsic semiconductorsare joined, as shown in Figure 4.1.

Figure 4.2 shows a sinusoidal power supply with a peak output of 3.0 V at a frequency of50 Hz. The power supply is connected to a 68 load resistor. The p.d. across the loadresistor is displayed on an oscilloscope.

North pole of electromagnet South pole of electromagnet4.00 cm

4.00 cm

p n

Figure 4.1

oscilloscope

68

Figure 4.2

3.0V peak50 Hz


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(a) Explain how the p-n junction acts as an open or closed switch in the circuit as thevoltage varies. You may draw a diagram if you wish.

[4

(b) The oscilloscope is set to a voltage sensitivity of 1.0 V cm-1. The trace in Figure 4.3 isseen on the grids of the oscilloscope. Calculate the average power dissipated in the

load resistor.2.4 V; 0.021 W

[3

5 Figure 5.1 shows an experimental arrangement used to estimate the activity of aradioactive source which emits -particles.

The following count-rates, as detected by the Geiger-Muller tube, are taken at twodifferent times t. Note that background-count has been established to be 50 min -1.

t/ hour count-rate / min-1

0 3248

6.0 851

0.80% of the -particles leaving the source are recorded by the counter. Each -particleproduces a count of one.

(a) Determine the activity of the source at the start of the experiment.6600 Bq

[2]

670 counterGeiger-Muller tube

source Figure 5.1

Figure 4.3

1 cm

1 cm


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(b) Determine the half-life of the source.3.0 h

[2]

(c) Counting is ended when the recorded count-rate falls to less than 100 min-1.Determine the time after the start of the experiment at which this occurs.18.0 h

[2]

6 (a) (i) 1. What is meant by internal energyof a system? [1]

2. Explain how the concept of internal energy is applied to an ideal gas ascompared to a real gas. [2]

(ii) The following is an excerpt from American Scientific (May 2009):

Many of the gases that make up Earths atmosphere and those of the otherplanets are slowly leaking into space. This leakage explains many of the solar

systems mysteries. For instance, Mars is red because its water vapour gotbroken down into hydrogen and oxygen, the hydrogen moved at higher speedsand drifted away, and the remaining oxygen reacted with rocks to form rust,and gives Mars its characteristic red colour.

Explain the following.

1. Hydrogen molecules are faster-moving than oxygen molecules. [2]

2. Fast-moving molecules are able to escape. [1]

3. Some oxygen molecules are also able to escape. [1]

(b) 1.00 x 10-2 mol of neon gas is contained in a vessel capped by a light moveablepiston. At equilibrium the volume enclosed by the vessel is 250 cm3. Take the massof a neon atom to be 20.0 u and atmospheric pressure to be 1.01 10 5 Pa. Assumebehaviour of the gas to be ideal.

(i)Using 2

1p = c >

3, where pis the pressure of the gas, is the density of

the gas, and is the mean-square speed, calculate the root-mean-square

speed of the neon atoms.616 ms-1

[3]

(ii) The vessel is submerged in a pure ice-water mixture and allowed to come tothermal equilibrium with its surroundings. The piston settles at a new position,X.


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Figure 6.1

1. Explain what is meant by thermal equilibrium. [1]

2. Calculate the change in the volume of the gas in the vessel.- 25 cm3

[2]

(iii) The gas is subjected to a cycle of changes A B C A as shown in Figure6.3.

A B: The piston is quickly pushed down from position X to position Y. Youcan assume that this process takes place so quickly that there is no heattransfer with the surroundings.

B C: The piston is held at position Y until the gas is again at the temperatureof the ice-water mixture.

C A: The piston is slowly raised back (such that there is ample time for heat

transfer between the gas and its surroundings and there is no temperaturechange in the gas) to position X.

Figure 6.2 Figure 6.3

1. The first law of thermodynamics can be expressed as

U= Q+ W,

pressure

volume

C

B

A

Position X

Ice andwater

Ice andwater

Y

X


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where Uis the increase in internal energy, Qis the heat supplied and Wisthe work done on the system.

Complete the following table. Use + to indicate a positive change in the

quantity, a to indicate a negative change in the quantity and 0 toindicate no change in the quantity.

U Q W

A B:

B C:

C A:

Entire Cycle[4]

2. The cycle is repeated many times. If 2.00 g of ice is melted by this action,calculate the total work done on the gas. Show your working clearly. Takethe specific latent heat of fusion of ice to be 3.36 10 5 J kg-1.672 J [3]

7(c) Figure 7.2 shows the energy level diagram of a three-level laser. Lasing takesplace between E2and E1.

(i) State the unique characteristic of energy level E2 that is important in theoperation of this laser. [1]

(ii) Explain the general action of the laser represented by Figure 7.2 in terms ofpopulation inversionand stimulated emission.

[4]Atoms in the ground state are excited to E3. These quickly de-exciteto the upper laser level E2.

When more atoms are in the upper laser level than in the groundstate (i.e. lower laser level), population inversion is producedbetween the upper and lower laser levels.

1

Ground state

E2

E1

E3

Figure 7.2


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When a photon of energy equal to E2E1 passes through the lasermedium, it can either be absorbed to cause excitation from E1 to E2or stimulate de-excitation from E2 to E1, releasing another photon ofenergy E2 E1 in the process. With population inversion, de-excitation is more probable than absorption. Stimulated emission

produces photons of the same phase, energy, frequency,polarization and direction of travel as the incident photon.

The photons are sent back and forth in the laser medium (by mirrorreflection) and in the process they will cause more stimulatedemissions.

2

1

(iii) Figure 7.3 shows the energy level diagram of a four-level laser. Lasing takesplace between E3and E2.

What is the advantage of the four-level laser over the three-level laser?Lower laser state is not ground state. After atoms move from the upper laserlevel (E3) to the lower laser level (E2) through stimulated emission, they will

quickly depopulate to the ground state (E1). This reduces the loss ofphotons by absorption between the upper (E3) and lower (E2) laser levels.

[1]

8 (a) The radioactive isotope of Bismuth, 21083Bi decays into Polonium (chemical symbol:

Po) with the emission of a beta particle.

(i) What is a beta particle? [1]

(ii) Write down the equation representing the beta decay of 21083Bi .[1]

(iii) State two quantities that are conserved in any radioactive decay process. [2]

(iv) The mass of a 21083Bi nucleus is 209.939 u. Show that its mass defect is

1.767 u. (mass of proton, mp = 1.00729 u; mass of neutron, mn = 1.00867 u )

[2]

(v) Hence calculate the binding energy, in MeV, of 21083Bi .

1646 MeV

[2]

Ground state

E3

E1

E4

Figure 7.3

E2


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(b) James Chadwick, in some experiments conducted prior to World War I, used aGeiger Counter to study beta particles emitted from a source and deflected by auniform magnetic field. He found that the beta particles had a wide range of radii ofcurvature in the field, indicating that the beta particles were emitted with adistribution of energies rather than with a distinct single value of energy.

Figure 8.1 shows the energy spectrum for beta particles emitted during the decay ofBi-210. The intensity (vertical axis) indicates the number of beta particles emittedwith each particular kinetic energy (horizontal axis).

Figure 8.1

(i) 1. Determine, from Figure 8.1 above, Q, the maximum possible energy of the

beta particle emitted from 21083Bi .

1.2 MeV

[1]

2. Hence calculate the velocity of the beta particle.6.5 x 108 ms-1

Comment on the value you obtained. [2]

3. Using values in (b)(i)1. and (a)(iv), determine the mass of the resultantPolonium nucleus, in units of u, and express your answer to 3 decimalplaces.

209.937 u[3]

Energy spectrum

of beta particlesemitted from 210Bi


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6 In the interior of the Sun, nuclear reactions take place whose net result is theconversion of hydrogen into helium with the release of energy. The three stagesin this proton-proton cycle are as follows:

reaction (1): eHHH 012

1

1

1

1

1 +++

reaction (2): ++ HeHH3

2

2

1

1

1 reaction (3): HHeHeHe 11

4

2

3

2

3

2 2++

The masses of the nuclei are:

H1

1 :1.00728u, H2

1 :2.01355u, He3

2 : 3.01493u, He4

2 : 4.00151u.

The mass of the positron e01+ is 0.00055u.

6(a) For there to be two He32 nuclei available for reaction (3), the first two reactions

must take place twice. What is the total energy released in the creation of a

single helium-4 nucleus from protons? [4]3.96 x 1012 J

6(b) The first stage in the process is the fusion of two hydrogen nuclei. Why is energyneeded to do this? [1]

6(c) When hydrogen is raised to high temperatures, it dissociates into atoms and isionized. Assuming that hydrogen ions behave like an ideal gas inside the Sunscore, estimate the temperature required for the hydrogen ions to achieve anenergy of 1.0 MeV in order for fusion to take place. [2]

3.87 x 109 K

6(d) Why are these reactions sometimes called thermonuclear reactions? [1]

NJC P3

4(a) Describe one piece of evidence based on the observations from the photoelectriceffect experiment to support the particulate nature of electromagnetic radiationwhen it interacts with matter. [2]

(b) The stopping potential for electrons emitted from a metallic surface illuminated bylight of wavelength 480 nm is 0.64 V. When the incident wavelength is changedto a new value, the stopping potential is 1.30 V.

Calculate(i) the work function for this metallic surface, [2]

3.12 X 10-19 J(ii) the new wavelength. [1]

383 nm


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(c) A 1500 kg car moving at 25 ms-1 approaches a hill that is 40 m high and 30 mwide. The hill can be regarded as a potential barrier where the potential energy isgravitational. If the car were a matter wave approaching a potential barrier,calculate

(i) the gravitational potential energy of the car at the top of the hill,[1]

5.89 x 105 J

(ii) the transmission coefficient of the car, if it could tunnel through the hill.Leave your answer in terms of the exponential e. [2]

exp (- 1.08 x 1040)

5 A spray can contains liquid paint with compressed gas in thespace above it, as shown in Fig.5. Pressing down the cap opensa valve which allows the gas to expand, forcing paint through thenozzle. The cap is pressed until all the paint is expelled, leaving

the can filled with gas at a pressure which is still greater thanatmospheric.

(a) The can has an internal volume of 6.6 10-4 m3 and initially

contains 5.0 10-4 m3 of paint. The gas in the can is at an initial

pressure of 7.8 105 Pa. The pressure of the gas left in the can

when all the paint has just been expelled is 1.9 105 Pa. Showthat the expansion of the gas is approximately isothermal. Statean assumption used in your calculation. [3]

(b) 1. Define specific heat capacity. [1]

2. Describe an experiment in which the specific heat capacity of an unknownpiece of metal of a certain mass could be determined with the use of anelectrical heater of known power. [4]

(c) The line ABCD in the graph below is the indicator diagram for a particular engine.

Fig.5


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(i) Explain whether thermal energy is taken in or given out by the engine forthe process B. [3]

- 9000 J

(ii) Determine the net work done by the engine during the cycle ABCD. [3]20 kJ

(iii) The useful output power of the engine is equal to the rate of net workdone by the engine. If the engine is running at 3 cycles per second,determine useful output power. [2]

60 kW

(iv) This engine obtains its input energy from burning fuel of calorific value 34MJ kg-1 at a rate of 2.4 10-2 kg s-1. Calculate the efficiency of the engine.0.0735 [3]

(iv) The line ABED in the graph is the indicator diagram for the same engineafter a modification has been made. Without further calculation, comparethe performance of the modified engine with that of the original enginewhen both engines are making the same number of cycles per second.

[1]

A

B

C

D


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TJC P2

6 (a) Define binding energyof a nucleus. [1]

(b) (i) 126 C and

136 C are two different isotopes of carbon. Calculate the binding energy

per nucleon, in MeV, of the two isotopes, given the following data:

mass of 126 C = 12.000000 u

mass of 10 n = 1.008665 u

mass of11H = 1.007825 u

mass of 136 C = 13.003355 u

(c)

(ii)

(i)

7.70 MeV; 7.49 MeV

Hence, state and explain which of these two isotopes is more stable. [1]

Sketch a graph showing the variation with the mass number of the bindingenergy per nucleon. Mark with a cross (x) a point on your graph which

A

B

E

D


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represents the most stable nuclide. [3]

(ii) Hence explain why fusion of nuclei having high nucleon numbers is notassociated with a release of energy.

TJC P3

4 (a) A bar magnet is suspended from the free end of a helical spring as shown in Fig. 4.1.A pole of the magnet is situated near to one end of the solenoid.

Fig. 4.1

State and explain the motion of the magnet

(i)when a direct current in the solenoid is switched on, and [2]

(ii) when an alternating current passes through the solenoid. [3]

(b) In Fig. 4.2, a 10 MW nuclear power station produces electrical voltage at600 V. It uses a step-up transformer with a turns ratio of 1: 200 toincrease the voltage before transmitting it over long-distance cables oftotal resistance 15 .


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Fig. 4.2

Calculate the power lost as heat in the cables.1.04 x 105 W

6 (a) (i) Explain what is meant by the term internal energyof a gas. [1]

(ii) What additional fact may be stated about the internal energy of a gas if the gas

is ideal? [1]

(b) 1.0 mole of helium gas, assumed to behave ideally, is contained within a metalcylinder which is not insulated. The cylinder has a frictionless piston, as shown inFig. 6.1.

Heat is supplied to the gas and its temperature changes from 20 C to 120 C.

(i) Show that the change in the internal energy of the gas 1250 J. [2]

(ii) Calculate the increase in volume of the helium gas as a result of the rise intemperature from 20 C to 120 C if the gas is maintained at the atmosphericpressure of 1.01 x 105 Pa. [2]

8.23 x 10-3 m3(iii) Calculate the heat that has to be supplied to the gas in the cylinder for the

expansion described in (ii) to occur. [3]2080 J

(c) The helium gas in (b) is then compressed back to its initial volume by applying anexternal force on the piston. The process is carefully controlled so that the

temperature of the helium gas remains constant at 120 C.

(i) Calculate the final pressure of the gas. 1.36 x 105 Pa [3]

1 mole of helium gas

Fig. 6.1

piston


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(ii) State whether heat energy will be absorbed or given out by the gas in theprocess described in (c)(i). Explain your answer. [3]

(d) An electric kettle, rated 240 V 5.0 A, contains some water. The kettle is switched on

and the temperature of water is found to rise at the rate of 9.0 C per minute. Thespecific heat capacity of water is 4.2 103 J kg-1 K-1.

(i) Calculate the mass of water in the kettle. [3]1.9 kg

(ii) State and explain whether your answer to (d)(i) is greater or smaller than theactual mass of the water contained in the kettle.

7 (a) (i) Explain the meaning of the term diffraction. [1]

(ii) How does the width of the aperture through which a wave is passing affect thediffraction of the wave? [1]

(b) A progressive sound wave of wavelength is incident on an open pipe as shown in

Fig. 7.1. The length of the pipe is . A stationary wave is formed in the pipe.

Fig. 7.1

(i) Describe the formation of the stationary wave in the pipe. [2]

(ii) On Fig. 7.1, sketch the shape of the stationary wave in the pipe. Mark thepositions of the nodes and antinodes with the letters N and A respectively. [2]

(c) (i) Electromagnetic waves have a wave nature as well as a particulate nature.Briefly describe a situation in which particles can be shown to have a wavenature. [1]

(ii) Calculate the wavelength of a particle of mass 1.82 10 -28 kg and kinetic energy8.2 10-14 J. [3]1.21 x 10-13 m

direction of

incident wave


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(iii) If the position of the particle can be determined to within the wavelength youhave calculated in part (ii), determine the uncertainty in the particles momentum.4.36 x 10-22 Ns [2]

(d) Fig. 7.2 represents part of the emission spectrum of atomic hydrogen. It contains aseries of lines in the ultraviolet region, two wavelengths of which are marked. There

are no lines in this series with wavelengths less than 91.2 nm.

91.2 121.6 /nmFig. 7.2

(i) Calculate the photon energies corresponding to the wavelengths marked.

1. 91.2 nm

2.18 x 10-18 J

2. 121.6 nm1.64 x 10-18 J

[3]

(ii) With the aid of an energy level diagram, explain why the lines in the series getcloser for smaller wavelengths. [2]

(iii) Explain why it is that although there are an infinite number of lines in thisspectrum, the spectrum is nevertheless seen as a line spectrum. [3]

(iv) Electrons emitted by a hot filament pass through a tube containing hydrogen gasand are then collected by an anode which is maintained at a positive potentialwith respect to the filament. The gas is found to emit monochromatic ultravioletradiation. Suggest a reason why the radiation is monochromatic. [1]


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VJC P2

4. The setup in Fig. 4.1 shows the top view of a 12 V DC supply connected in series with

a rod PQ of length 0.50 m. The rod has a resistance of 24 . The frictionlessconnecting rails are very long and have negligible electrical resistance. The rod lies ina region of a uniform magnetic field. The magnetic field strength is 1.0 T and the

direction of the field is perpendicular to and acts into the plane of the page. The twoends of the rod rest on the rails and are free to move in the plane of the rails. The rodis initially at rest.

12 V

rod

Q

Conducting rail

switch

P

Y

Z

Conducting railFig. 4.1

magnetic field

acts vertically

downwards

Fig. 4.2 shows the side view of the setup. The conducting rails are inclined at anangle of 30o above the horizontal.

Fig. 4.2

30o

rodI

B = 1.0 T

Q

Y

I Conducting rail

The mass of the rod is 20 g.

(a) On Fig. 4.2, draw the forces acting on the rod. [1]

(b) Calculate the initial acceleration of the rod when the switch is closed, and state itsdirection. [3]

5.9 ms-2 up the slope

(c) Calculate the circuit current when the rod reaches terminal velocity. [2]

0.23 A(d) The moving rod PQ functions like a source of e.m.f. Identify the end of the rod (P

or Q) which is at the higher potential. Explain your answer. [2]


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5. Two blocks of copper are maintained at the same positive electrical potential of +4.00

V. If they are brought close together, until their separation is 5.00 10-10 m, then thereis a finite probability that an electron from either block will tunnel across the gapbetween them and appear on the other side.

(a) Calculate the electrical potential energy of an electron in either of the two blocks,

expressing your answer in electron-volts. Take the potential energy of theelectron at an infinite distance away from the blocks to be zero. [2]

- 4.0 eV

(b) Draw a diagram to show how the electrical potential energy of an electron variesas it moves from a point inside one block across the gap to a point inside theother block. Take the potential energy of the electron in the gap to be zero. [1]

The transmission coefficient T for an electron to tunnel across a potential barrier of

width d is given by T exp(2kd), where

)(2 0 EVmk

= , with mbeing the

mass of the electron, V0 being the height of the barrier and Ebeing the total energyof the electron.

(c) When electrons of energy 1.0 eV approach the gap from within the block, theprobability of successful tunnelling is T. If the width dof the gap is increased by

10 %, determine the new value of the energy Eof the electrons such that theprobability of successful tunnelling remains at the same value T. [3]

1.52 eV

(d) A stream of electrons of the same energy hits the above barrier at a rate

equivalent to a current of 4.00 A. If it is known that the probability of successfultunnelling is 1.83 10-12, determine the rate of tunnelling of electrons through thebarrier. [2]

45.8 s-1


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4. In a photoelectric emission experiment, a metal surface in an evacuated tube wasilluminated with light. The graph below shows the stopping potential as a function ofthe frequency of the incident light falling on the metal surface.

(a) Deduce a value of Plancks constant from Fig. 8.1. [3]6.6 x 10-34 Js

(b) Determine the work function for this metal, expressing it in electron-volts. [2]5.4 eV

(c) Explain the observation that the graph in Fig. 8.1 does not extend below thehorizontal axis. [1]

(d) The work function of a metal in air increases over time. Suggest a reason why. [2]

5. (a) In a ruby laser, a xenon discharge lamp surrounding a ruby crystal supplies lightenergy to the chromium atoms inside the ruby crystal in a process called opticalpumping. Fig. 5.1 shows the energy levels of chromium atoms embedded in theruby crystal.

2.20

1.79

0

electron energy /

E0 (ground state)

E1

E2

Fig. 5.1


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(i) With reference to Fig. 5.1, deduce the wavelength of the light from the xenonlamp that is absorbed by the chromium atoms during optical pumping. [2]

565 nm

(ii) Calculate the wavelength of the laser light emitted by the chromium atoms. [1]694 nm

(iii) Explain why the power supplied by the xenon lamp via optical pumping mustexceed a certain minimum value before the ruby laser produces laser light ofusable power. [2]

(b) Scientists are trying to fuse isotopes of hydrogen together with the useof lasers, in an effort to produce clean renewable energy. In such experiments,many laser beams are focussed onto a tiny pellet of fuel containing 1.00 10-4 kgof deuterium (an isotope of hydrogen with one proton and one neutron). In orderfor the deuterium nuclei to fuse and produce nuclear energy, the temperature ofthe fuel pellet must be raised to around 1.00 108 K in a short time of about 1.00 10-12 s.

Determine the power of the laser system needed for such nuclear fusion to occur.(Hint: You may assume that the deuterium behaves like an ideal gas after it isvaporised by the laser beams.) [3]

6.19 x 1019 W

7.(a) (i) Explain what is meant by internal energy of a system. State what constitutes theinternal energy of an ideal gas. [2]

(ii) State two factors which determine the internal energy of an ideal gas. [2]

(iii) An ideal gas is kept in a sealed container in a car which suddenly increases inspeed. Discuss whether the internal energy of the gas will increase. [2]

(b) Evaporation of sweat is an important mechanism for temperature control in humans.

(i) Using a simple kinetic model for matter, explain how evaporation of sweat canhelp in temperature control in humans. [2]

(ii) A 60.0 kg runner expends 300 W of power while running a marathon. Assumingthat 10 % of the energy is delivered to muscle tissues and that the excessenergy is primarily removed from the body by sweating, determine the volumeof bodily fluid (assume it is water) lost per hour. Take the specific latent heat of

water to be 2.41 106 J kg-1. [3]4.03 x 10-4 m3 h-1

(iii) Suggest, with a reason, whether the runner loses the amount of sweatcalculated in (ii) in a practical situation. [2]

(c) A scuba diver descends to 8.2 m below the surface of the sea.

(i) Estimatethe pressure (in atmospheres) that her scuba-diving tank regulatorwould need to supply so that her lungs can fill as normal. [2]

1.8 atm


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(ii) Calculate the ratio of the number of air molecules in her lungs at a depth of 8.2m to the number of molecules in her lungs at the surface. [2]

1.8(iii) State an assumption made in the calculations in (ii) [1]

(iv) If the diver ascends too quickly, bubbles will form in his blood, a painful andpotentially dangerous situation known as the bends. Suggest how this couldcome about. [2]

8. (a) Describe how two samples, one emitting alpha particles, and the other emittingbeta particles can be distinguished through a simple school laboratory experiment,using a Geiger-Muller (GM) tube connected to a ratemeter. [3]

(b) Radon (Rn) decays spontaneously with a half-life of 52 s to form polonium (Po)and polonium in turn decays spontaneously with a half-life of 0.16 s to form lead(Pb).

Rn22086 Po216

84 Pb212

82

52 s 0.16 s

X

(i) Define the terms activityand decay constant. [2]

(ii) State the identity of the particle labelled X and write down the first decayequation in the series in (b). [2]

(iii) Suppose the activity of radon, Rn, is determined by measuring the number of

particles X emitted. Explain how the decay of 21684

Po will affect the

measurement. [3]

(c) Radioactive isotopes are often introduced into the body through the bloodstream.Their spread through the body can then be monitored by detecting the appearanceof radiation in different organs. Iodine-131 (131I), a beta emitter with a half-life of8.04 days, is one such tracer. Suppose a scientist introduces a sample of 131I withan activity of 375 Bq into the body and watches it spread to the organs.

(i) Discuss the difference between a photoelectron and a beta-particle by makingreference to their origin. [2]

(ii) Assuming that all of the 131I atoms in the sample went to the thyroid gland,calculate the decay rate in the thyroid 2.5 weeks later. Assume that none of the131I is eliminated by the body through physiological means. [3]

82.9 Bq

(iii) Calculate the mass of 131I required to produce an activity of 375 Bq. [3]8.2 x 1017 kg

(d) State one similarity and one difference between radioactive decay and nuclearfission. [2]

Documents

Thermal, Emi and Modern Physics Revision 1